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If a = c*10^b and a and b are integers, what is the value of b?

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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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If a = c*10^b and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
(2) 1 < b < 4

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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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Bunuel wrote:
If a = c*10^b and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
(2) 1 < b < 4


Statement 1: \(c=0.xyz\), where \(x,y,z\) are digits in tenths, hundredths, and thousandths places but nothing mentioned about \(a\) or \(b\). Hence \(insufficient\)

Statement 2: \(b\) can be \(2\) or \(3\). Hence insufficient

Combining 1 & 2. \(a = c*10^b\),

or \(a= 0.xyz*10^b\) we know that \(a\) is an integer, hence \(b=3\) because if \(b=2\) then \(a=xy.z\) which is not an integer. Hence sufficient

Option C

Originally posted by niks18 on 03 Oct 2017, 01:20.
Last edited by niks18 on 15 Oct 2017, 01:00, edited 2 times in total.
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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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New post 03 Oct 2017, 01:39
If \(a = c*10^b\)and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
=> This tells us that c is a 3 digit decimal number => c = 0.pqr ( p,q,and r are single digit integers)

to make 'a' as an integer 'c' need to be multiplied by 1000 => minimum value of a => \(a = c*10^3\)
Here as we don't know value of a => b can take any value greater or equal to 3 => \(b\geq{3}\)
Insufficient

(2) 1 < b < 4
as b is an integer => b = 2 or 3
Insufficient

1+2

=>by statement 1=> \(b\geq{3}\)
by statement 2 => b = 2 or 3
=> b=3

Answer: C
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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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New post 03 Oct 2017, 06:01
(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?
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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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New post 03 Oct 2017, 06:12
kunalsinghNS wrote:
(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?


Hi kunalsinghNS

it is mentioned in the statement that ONLY tenths, hundredths, and thousandths places have non zero digits
So \(c=0.234\) or \(c=10.897\). In either case if you multiply \(c\) by \(10^3\), then it will become an integer
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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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New post 03 Oct 2017, 07:54
kunalsinghNS wrote:
(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?


Please refer attached figure and below mentioned line, it might help.

c has nonzero digits in only the tenths, hundredths, and thousandths places.
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Number.jpg [ 16.72 KiB | Viewed 824 times ]

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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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New post 03 Oct 2017, 18:53
Thank you for the explanation niks18 and Nikkb
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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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New post 29 Mar 2018, 01:11
It will help if you catch the difference
tens-tenth
hundreds - hundredth
thousands - thousandth
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Re: If a = c*10^b and a and b are integers, what is the value of b? &nbs [#permalink] 29 Mar 2018, 01:11
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